i am given {An} , {Bn} so
An->a
Bn-An->0
prove that Bn->a
??
Is this in or in a generalized metric space? Ill assume its the former.
We know that by the definition of a convergent sequence that if then there exists such that if then
So we have that there exists a such that implies that
And that there exists a such that if then
Now it should be pretty apparent that since the metric on is that
So now consider
For